Answer
See below.
Work Step by Step
Using the given identities: $\csc^2(x)(1-\sin^2(x))=(\frac{1}{\sin(x)})^2(\cos^2(x))=(\frac{\cos(x)}{\sin(x)})^2=\cot^2(x)$.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.